Math (geometry)

posted by .

Line l is tangent to circle O at point P(3,4) where the center is located at (0,0).
a. Find the radius of the circle. (I got 4)
b. Give an equation of the circle. (I got x^2+y^2=16)
c. Find the slope of line l.
d. Give an equation of line l.
---------------------------------------------------------------------------------------------------

I can't figure out what the slope would be, if I knew that I could figure out (d). Does anybody know how to do this?

  • Math (geometry) -

    Since the line is tangent at a point to the circle, then the point lies on the circle. Also, since you know the center, the radius is simply the distance between the points (0,0) and (3,4).

    a) So, radius=d=sqrt((3-0)^2+(4-0)^2)=5
    b) x^2+y^2=25
    c) Observe that the radius is perpendicular to the tangent line. Thus, if you can find the slope using the coordinates of endpoints of the radius (i.e. (0,0) and (3,4)) then the negative reciprocal of this value will give the slope of the tangent line. Answer is -3/4.
    d) Since you know the slope (-3/4) and the point (3,4) is on the line, we can use the form y=mx+b. If you go through the motions, you'll find that y=(-3/4)x+(25/4)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calc

    standard equation of circle concentric with X^2+Y^2-2X-8Y+1=0 and tangent to line 2X-Y=3 Complete the squares to find the center of the circle. X^2+Y^2-2X-8Y+1=0 (x-1)^2+(y-4)^2 - 16 =0 The center is (1,4) and the radius for the given …
  2. Math

    I have a series of questions that I did. They lead up to the last question I can't solve. Could you check my math and help me with the last question?
  3. GEOMETRY INSCRIBED ANGLES MULTIPLE CHOICE QUESTION

    segment BC is tangent to circle A at B and to circle D at C. (Not drawn to scale) AB=10 BC=25 and DC=3. Find AD to the nearest tenth. Hint: Draw an auxiliary line from D to segment BA. {There are two circles, the larger one has point …
  4. Math

    Answer check please: Consider the circle (x-3)^2 + (y+1)^2 = 169. The point (15,4) is on the circle. Find an equation for the line that is tangent to the circle at this point. I got y= 5/12x-9/4.
  5. mathematics

    The circle x2-2x+y2-4y-4=0 lies on the cartesian plane,question 2.1.1 equation of new circle which is the rotation of original circle through 180 degree around the origin...2.1.2 find equation of another circle which is the translation …
  6. mathematics

    The circle x2-2x+y2-4y-4=0 lies on the cartesian plane,question 2.1.1 equation of new circle which is the rotation of original circle through 180 degree around the origin...2.1.2 find equation of another circle which is the translation …
  7. mathematics

    The circle x2-2x+y2-4y-4=0 lies on the cartesian plane,question 2.1.1 equation of new circle which is the rotation of original circle through 180 degree around the origin...2.1.2 find equation of another circle which is the translation …
  8. GEOMETRY CIRCLES PLEASE

    1.An isosceles triangle with each leg measuring 13 cm is inscribed in a circle . if the altitude to the base is 12 cm find the radius of the circle 2. Circles a and b are tangent at point c. p is on circle a and q is on circle b such …
  9. GEOMETRY CIRCLE

    1.An isosceles triangle with each leg measuring 13 cm is inscribed in a circle . if the altitude to the base is 12 cm find the radius of the circle 2. Circles a and b are tangent at point c. p is on circle a and q is on circle b such …
  10. math

    The center of a circle is located at (–5, 2) and a point on the circle is located at (5, -22). Which other points are also on the circle?

More Similar Questions